I plan to buy two microphones, one for voice and one for the instrument, but I don't know what microphones would be best. I found some good suggestions here (http://home.earthlink.net/~rongonz/home_rec/microphone.html) but I'm still looking for more guidance. I'm looking in the sub-$100 range. Then there's the problem of recording the two separate tracks onto the computer. From what I understand, I can record two tracks using a normal sound card's line-in feature, sending one track to the left stereo channel and the other track to the right channel. However, I'd need a powered mixer to provide enough juice to the microphones, because the sound card's wimpy 1/8" line-in jack won't give enough power to work the mikes, right?--but from what I understand, even a cheap $30 mixer will do the trick. Are these assumptions correct? Or should I get a different sound card, or a USB/Firewire device? Or are there any other recommendations you would give to a relative newbie when it comes to prosumer audio recording equipment?

You need to start with a good microphone. You don't need to go crazy on a large diaphram condensor or anything, though. A Shure SM-57 should do nicely. You can pick one up for $90 - $100 usually. A boom stand will cost you another $60 - $120. You can probably get away with a cheaper stand if you're the only one using it. Depending on the route you want to go, you'll either need a mixer or an audio interface for your PC. For mixers, the best bang for your buck is the Yamaha M-series. They're cheap, lightweight, compact, and sound quite nice. You won't get much in the way of EQ controls on it, though. For multitracking on PC, M-Audio makes some cost-effective gizmos. ProTools is the industry choice, but it's quite pricey. If you're going to do the digital thing (recommended), you'll need multitracking software. I like N-Track Studio. It's no Wavelab, but it does the job for about $70. Otherwise, you'll need a good recorder. I recommend Denon--I've never had any trouble with their gear. That's enough to get you started. You may eventually want to add a simple MIDI keyboard--even if you can't play the piano at all, it's still handier than trying to write a MIDI roll with the mouse. Processing can be taken care of inside the PC, but sometimes a physical EQ is easier to deal with. You can make some poor man's acoustic treatment with "finger foam"--that ridged foam packing material. Glue it to large plywood panels, and you can gain a little bit of control over what sounds hit your microphone.

I hope you have given a lot of thought to the room you are using. It needs the proper sound proofing/enhancing wall coverings. Ideally, there should be no windows, or they should be properly covered. If the ceiling is too low, it can inhibit the proper sound, and needs baffling.

I don't seem to be able to post this in the comments for some reason, so I'll make it a new answer. RCA cables are simply poorly designed. Ordinary wear-and-tear causes the two "shell" pieces on the plug to separate until they no longer provide a solid connection. It's simple enough to press them back into shape, but why risk losing what might have been a good take? Also, the wires tend to break at the point the cable enters the connector. 1/4" is slightly better than 1/8", but only because the wires are usually bigger, therefore more durable. The cable you linked to will be a bit better than the one I pointed to, simply because you have one fewer connections and thus one fewer points of possible failure. Finally, the properties of the wire will not generally affect the quality of the sound, no matter what the audiophiles and Monster's salespeople tell you. The important factors are how long the cable will last and how good the connectors are.